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math.GN2023
Vietoris endofunctor for closed relations and its de Vries dual
Marco Abbadini, Guram Bezhanishvili, Luca Carai
We generalize the classic Vietoris endofunctor to the category of compact Hausdorff spaces and closed relations. The lift of a closed relation is done by generalizing the construct…
math.GN2023
A New Proof of the Joyal-Tierney Theorem
Guram Bezhanishvili, Luca Carai, Patrick Morandi
We give an alternative, more geometric, proof of the well-known Joyal-Tierney Theorem in locale theory by utilizing Priestley duality for frames.
math.LO2023
Heyting frames and Esakia duality
Guram Bezhanishvili, Luca Carai, Patrick Morandi
We introduce the category of Heyting frames and show that it is equivalent to the category of Heyting algebras and dually equivalent to the category of Esakia spaces. This provides…